Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. C3×C8×C9 | Q8 | semidirect |
| 87. C8×C9 | Dic6 | semidirect |
| 129. C3×C9 | #501 | semidirect |
| 144. C3×C8 | Dic18 | semidirect |
| 176. C9 | #4702 | semidirect |
| 184. C8 | #6226 | semidirect |
| 198. C3 | #10588382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721707 | 2 |
| #11721706 | 2 |
| C3×C9×#97 | 2 |
| #11720541 | 2 |
| #11720540 | 2 |
| #10592401 | 3 |
| #10588382 | 3 |